INSP

INSP

Multiscale Mechanics of Softs Solids – Acoustic propagation in glasses


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  • Honorary research fellow: Christiane Caroli

In glasses, acoustic propagation presents  generic features thought to be  characteristic of topological structural disorder. Up to now, theoretical approaches to this question – fluctuating elasticity (FE) theories – assume heuristically thatvibrations in a glass are those of a continuum with spatially fluctuating elastic constants and, possibly, low frequencyscattering localized defects. They fail to capture, in particular, the observed anomalous  (~k d+1 logk) Rayleigh scaling of the sound damping coefficient. We have recently shown, by deriving FE as a long-wavelength approximation of the microscopic wave equations, that this deficiency must stem from their neglect of small scale non-affinity effects.

We are now developing a method which permits to rigorously derive the continuum wave equation from the microscopic one, using a projection formalism whcih separates long- and short-scale affinity effects. Acoustic excitations then explicitly appear as ’’phonons’’ which undergo disorder-induced scattering via two coupling mechanisms : (i) a direct one, responsible for weak FE-like effects (ii) an indirect one, mediated by propagation in the large-k subspace, the eigenstates of which play the role of scatterers -thus generalizing and making explicit the notion of ‘’dynamical defects’’.

This work should settle, we think, the long-standing issue of formulating wave propagation in amorphous media as an explicit scattering problem. It is in progress, but the method already shows that the continuum representation of soundpropagation in glasses should incorporate non-local elasticity effects, a point which has never been envisioned until now.

 

Main collaboration

  • Anaël Lemaître : IFSTTAR, Institut Navier, Ecole des Ponts ParisTech

 

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